155: Chapter 155 World Recalibrates Coordinates

August 24th, 11:17 PM.

Room 402, Building 17 of Zijing Apartment.

Jiang Lin logged into the preprint server.

He first opened the local verification tool, and the cursor flashed rapidly in the terminal window.

[PFR_Marton_v1.0_public.pdf]

The file was PFR/Marton v1.0-public after completing the public release packaging.

The main proof chain still used the hash-anchored version of the controlled circulation package, and the newly added parts were merely the navigation, C-2 description, formal verification guide, and version index of the public version.

The hash fingerprint was completely consistent with the public read-only mirror record.

Jiang Lin glanced at the time in the upper right corner of the screen, and the numbers jumped silently, changing to 11:18 PM.

He gripped the mouse and dragged the file into the upload window.

The title bar automatically filled in the paper name.

[Polynomial Freiman-Ruzsa in Finite Field Models and an Entropic Bridge to Marton's Form]

The author column had only one name.

Jiang Lin.

No advisor.

No research group.

No joint corresponding authors.

In this deep-water zone intertwined with Additive Combinatorics, information theory, and probability theory, he was a lone traveler.

In the affiliation column, Jiang Lin thought for a moment, tapped the keyboard, and filled in two lines.

Yau Mathematical Sciences Center, Tsinghua University.

Qiuzhen College, Tsinghua University.

Starting today, this public version of PFR/Marton v1.0 would be undertaken by the Mathematical Sciences Center of Tsinghua University to host discussions, archive feedback, and organize digestion.

And Jiang Lin himself was indeed already a 2022 undergraduate student at Qiuzhen College of Tsinghua University.

In the abstract box was the English text he had repeatedly revised and deleted.

Finite Field Model.

Polynomial Freiman-Ruzsa main proof closure.

Marton entropy form bridge connection.

Degenerate case index.

Isolation of duplicate payments under non-uniform density shells.

He didn't blow it up larger to claim solving all cases under abelian groups.

Nor did he hide it smaller to cover up the astonishing fact that it crossed the quasi-polynomial barrier within the Finite Field Model.

After confirming everything was correct, Jiang Lin clicked submit.

The progress bar reached the end.

The page refreshed.

The preprint number was generated.

The public link appeared.

Jiang Lin copied the link, opened his email client, and sent the link to the archive email of the Mathematical Sciences Center of Tsinghua University, while simultaneously synchronizing it to Professor Han Yanshan, Ding Jian, Professor Lin Zhaoye, Professor Gu Nanzhou, and several overseas scholars who had previously entered the controlled review chain.

The email body had only three lines, resembling a system execution log.

[PFR/Marton v1.0 public version uploaded.]

[The file hash matches the controlled circulation package.]

[No further changes after release.]

After sending it, he closed the browser, brought up the terminal, and saved the system logs.

The local Git last commit record stopped at [release-public-v1.0].

Outside the window, the Tsinghua University campus was still sleeping in the night.

The distant tree shadows swayed gently in the breeze, and occasionally a few late-summer insect chirps came over.

Most freshmen were still catching up on sleep for the next day's military training. In their world, the biggest annoyance might just be whether tomorrow's sun would be too blazing or whether the instructors would be too strict.

But from this moment on, a preprint whose number had just been generated had transformed into a silent thunderbolt, splitting into the public view of the entire mathematical community.

At 12:29 AM.

At the Mathematical Sciences Center of Tsinghua University, the lights were still on in a PhD student office on the third floor.

PhD student Li Zhou was pulling his hair out in front of the dense tensor formulas on his computer screen.

His graduation thesis progress was slow, and he was currently on the verge of extreme anxiety and scattered attention.

To escape the formulas in front of him, he habitually opened the latest submission page of the preprint website and refreshed it aimlessly.

In recent days, the circulation of Jiang Lin's PFR/Marton manuscript in small discussion groups had been enough to stimulate the nerves of climbers like them at the bottom of academia.

There were whispers everywhere in the center, and many people knew that the legendary official public version would appear sooner or later.

But when he actually saw the page load and saw the long title occupying the top of the list, Li Zhou still froze for a moment.

The title was too long.

The author was too short.

He subconsciously clicked on the PDF link.

The network lagged for half a second, and then the first page loaded.

The title, author, abstract, and the densely and logically unfolded table of contents that followed. Li Zhou's gaze swept across Entropic Bridge in the abstract, and his heartbeat skipped a beat.

He hurriedly copied the link and forwarded it into the mentor group's large WeChat group.

After the message was sent, the read count in the group jumped from 1 to 15 in a mere ten seconds.

But no one replied.

One minute, two minutes.

The air seemed to have frozen.

Usually whenever an important preprint appeared, someone in the group would always crack a few jokes, post a background introduction, raise a few preliminary questions, or at least send a meme of 'bookmarking to read later' to liven up the atmosphere.

This time, completely none.

All small talk and polite pleasantries were suppressed by the enormous academic quality.

The dozen or so people behind the screens, including several full professors, clicked open the PDF at the same time, falling into that instinctive state of holding their breath and concentrating when facing a huge and unknown proof structure.

At 1:46 AM.

In the overseas academic mailing list, the first forward appeared.

The forwarder was Tom Sanders from the University of Oxford, one of the core figures in the field of Additive Combinatorics.

The email title was very short.

[Jiang's PFR/Marton preprint]

The body text was shockingly short, yet every word carried the weight of a thousand jin:

[The public version is now available. The finite-field PFR route crosses the old quasi-polynomial barrier in the stated model. The accounting is unusually explicit; this is not a sketch.]

"Not a sketch."

This sentence was like a heavy hammer, and was quickly screenshotted and sent back to the domestic academic circle.

In the mathematical world, sketch often meant a train of thought and a framework. Although valuable, it was still a far cry from a truly impregnable proof, and could collapse completely at any time due to a minor technical loophole.

And Sanders used unusually explicit to describe the account calculations in the text, which was an extremely high evaluation.

At 2:03 AM.

Terence Tao replied in the comment section of his WordPress blog to a netizen's related question about recent PFR rumors.

[In the stated finite-field setting, the main PFR chain appears closed. The remaining task for the community is no longer to locate an obvious missing step, but to digest the mechanism.]

When this reply was screenshotted and forwarded to major forums, the two words circled out by everyone first were:

closed.

digest.

The main chain was already closed.

The next step was not to find whether there were obvious gaps in the proof, but to digest this mechanism.

The subtext of this sentence was: "Jiang Lin's building has already been built; now it is up to us peers to understand how its load-bearing walls were designed."

At 2:27 AM.

Timothy Gowers (Fields Medalist) updated a short essay on his personal blog.

The title of the essay was: [A machine with closed accounts]

Gowers's writing style always carried the vividness and sharpness unique to British scholars.

He wrote ——

"When reading the first twenty pages of this manuscript, I tried to look for those little tricks in traditional Additive Combinatorics, but I failed. This is neither a one-page trick, nor a romantic story of some beautiful lemma suddenly piercing through the entire city wall; it is more like a complex heavy-industry machine. What is surprising is not that the machine is complex enough, but that the accounts are clear enough. The consumption of every degree of freedom and every entropy payment are recorded clearly and plainly under the non-uniform density shell, without any obviously attainable ambiguity."

As soon as this sentence was transmitted back to China, the mathematics section of Shuimu Community exploded directly.

Many people didn't understand PFR.

Nor did they understand Marton's entropy form.

Much less how H(X+Y) under the Finite Field Model controlled structural explosion through asymmetric distribution.

But at least they knew that Gowers wasn't someone who would easily endorse a machine that looked very complex.

A proof that could make Gowers describe it as a heavy-industry machine must have reached a terrifying precision in the engagement force of its internal logic.

At 2:41 AM.

Ben Green forwarded the preprint link.

He wrote only one sentence, yet it made countless PhD students researching this direction feel both desperate and excited.

[The entry point to PFR in Finite Field Models will need to be rewritten.]

(The entry point to PFR in Finite Field Models will need to be rewritten.)

At 3:06 AM.

Freddie Manners added in the same email thread ——

[The shell-account separation is not cosmetic; it is part of why the proof can be read.]

(The shell-account separation is not cosmetic; it is part of why the proof can be read.)

At 3:33 AM.

Shachar Lovett forwarded the link from the side of theoretical computer science, leading this storm from pure mathematics to computer science.

[Several equivalence chains around PFR and inverse theorems should be rechecked against Jiang's formulation.]

These voices, within a mere few hours, covered the globe like a huge and dense network.

Everyone truly at a critical node reached out from their most familiar direction and touched the newly appeared proof chain.

Then, one after another, they gave judgments in the same direction.

Within the stated scope, the main chain was closed.

At 3:52 AM.

Science popularization blogger Shen Yanqiu forwarded Terence Tao's reply.

In the previous live broadcast that sparked controversy across the entire internet, he had just said facing the lenses of tens of thousands of viewers that he had obtained the complete manuscript and read it carefully, but was not qualified to review it.

He also withstood the abusive barrage across the screen and said that the right of judgment was not in his hands, nor in the hands of any netizen.

Now, the right of judgment did not land in the form of a red-headed document or an official statement.

It pressed down simultaneously from California, from Cambridge, from Oxford, and from several different directions.

Tom Sanders.

Terence Tao.

Gowers.

Ben Green.

Freddie Manners.

Shachar Lovett.

Coupled with Professor Han Yanshan and Ding Jian domestically, who had long participated in the closed-door briefings.

It was not a formal appraisal.

But within the mathematical community, with people in several key directions independently offering similar judgments, the weight of it alone was already heavy enough.

Shen Yanqiu sat in front of his computer, watching the constantly fluctuating overseas feedback on the screen, his fingers hovering over the keyboard for a long time.

He did not open another live stream to ride this wave of astonishing traffic, nor did he write a long article analyzing just how great this paper was.

He only posted two sentences.

"Last night, I said that the power of judgment is not in my hands."

"Now, those truly qualified have begun to give their answers."

Less than a minute after this dynamic was posted, the comment section began to refresh frantically.

Yet Shen Yanqiu did not reply to a single comment again.

In front of a true giant mountain, maintaining silence was the best footnote.

Four-twenty in the early morning.

The homepage of the Shuimu Mathematics board had been completely flooded by PFR / Marton.

The dozen or so hot posts on the entire board were uniformly all discussions about Jiang Lin.

The hottest post had its heat marked in red, and the title was—

"Jiang Lin's PFR / Marton public version goes online, Terence Tao, Gowers, Sanders, etc., have spoken out"

The replies on the first few floors were extremely brief, carrying a kind of fanaticism of staying up late to witness history.

Floor One: "The preprint link is here. Enough said, I am going to wash my face and keep chewing on it."

Floor Two: "Brothers, this isn't the draft version circulating in the small group before. It's the officially public version, and the typesetting is as pretty as a work of art."

Floor Three: "Did you see Terence Tao's reply? main chain appears closed. This is practically a direct stamp of approval!"

Floor Four: "That remark by Gowers about the ledger being closed was too ruthless; it directly shut the mouths of many people who wanted to pick a bone."

Floor Five: "Ben Green said the entry point needs to be rewritten. This means that future textbooks and reviews will have this chapter rewritten."

Floor Six: "So right now, we are no longer discussing whether it's right or wrong?"

Floor Seven: "To the one above, it hasn't been a time when ordinary netizens can discuss right or wrong for a long time. Didn't you look at the wording of those bigshots? digest. They are now studying this proof mechanism."

Floor Eight: "Judging from now, the closed-door meeting held by Professor Han Yanshan and the others a few days ago should have already given a domestic judgment. No wonder the Center's side has been terrifyingly quiet these past few days; turns out they were brewing a massive ultimate move."

Floor Nine: "After Jiangs Brick, he has secured another major achievement. This speed is simply inhuman."

Floor Ten: "It's different. Jiangs Brick was a brick, but this time it's a bridge."

"Jiangs Brick was a brick, but this time it's a bridge."

This sentence was quickly voted to the highest likes, and even set as a signature by many people.

Because it was concise enough and accurate enough.

The satisfying point of Jiangs Brick lay in an extremely specific construction, crudely and directly smashing through a door that had been closed for many years in the aperiodic tiling problem.

It was stunning, but it was an isolated point of assault.

Whereas PFR / Marton was different.

One end of it was small doubling and structural compression.

The other end was entropy forms and degrees of freedom payment.

What it spanned across the middle was a deep-water zone jointly concerned by Additive Combinatorics, probability, information theory, and theoretical computer science.

It connected two continents that could previously only gaze at each other across the sea. Hereafter, countless researchers could use this entropy form to build a bridge and freely travel between these two fields, or even develop new theoretical mineral veins.

Six o'clock in the morning.

Room 402, Building 17, Zijing Apartment.

Jiang Lin's phone alarm rang right on time.

Without any hesitation, he turned off the alarm and sat straight up from the bed.

Outside the window, the sky was just beginning to brighten, and the grayish-blue morning light leaked in through the gaps in the curtains.

In the upper right corner of his vision, a set of countdown timers that only he could see was still silently ticking.

Jiang Lin glanced at his phone's email notification.

Unread emails had already exceeded one hundred.

There were automated archiving confirmation letters from the Mathematical Sciences Center.

There was a brief reply from Professor Han Yanshan: "Public version read, very good."

There were suggestions sent by Ding Jian on how to dissect the article's structure in subsequent seminar classes.

There were also dozens of emails from overseas scholars around the world whose names had once appeared in textbooks.

Jiang Lin put down his phone, walked into the bathroom to wash up, and changed into his military training uniform.

The camouflage jacket carried a slight stiff feeling after being sun-dried; mhm, very clean.

What was rather uncomfortable was that pair of canvas shoes; they still rubbed his feet a bit.

He sat down by the bed, reinserted the shock-absorbing insoles he had carefully cut last night back into the soles of the shoes, and then confirmed that anti-friction tape had been properly applied to his heels.

Then he picked up the military training cap on the table, placed it on his head, and pushed the door open to step out.

Ten past seven.

Qiuzhen Class 221 assembled at Zijing Playground.

The coolness of early morning had not yet completely dissipated from the air, but the atmosphere within the formation was noticeably much more restless than usual.

Many people had scrolled past Shen Yanqiu's live stream clips before going to bed last night. Waking up in the morning and opening their phones, they found that news of the official PFR / Marton preprint going online was overwhelming.

Several thunderously famous overseas names spoke up one after another, and major chat groups within Tsinghua University were forwarding the news with burning enthusiasm.

Many people were secretly sizing up Jiang Lin, who was standing in the back row of the formation, out of the corners of their eyes.

After a session of training, the instructor ordered the formation to dismiss and rest.

Zhao Chengyu shuffled over to sit next to Jiang Lin, two buttons of his camouflage collar unbuttoned, sweat still hanging from his temples, and red bloodshot eyes pressed behind his glasses lenses from staying up late.

He first unscrewed a bottle of mineral water and gulped down more than half of it before turning his head to speak, a hint of absurd amusement wrapped in his tone: "That version you posted last night—last night I originally wanted to look at the abstract, but later I found that I couldn't even touch the entrance behind the abstract."

"Specialization has its own domain."

Jiang Lin replied with a phrase and screwed the bottle cap back on.

"You have completely reset the reference system for our Grade 22 Qiuzhen cohort."

Zhao Chengyu twitched the corners of his mouth in self-deprecation.

"This week we are still agonizing over group isomorphisms in abstract algebra, and you directly demolished the entrance of PFR. That remark by Ben Green about the entry needing to be rewritten has been frantically forwarded by senior students this morning."

Jiang Lin raised his eyes to look at the instructor blowing the whistle not far away: "Assemble first."

Watching the other's completely unruffled expression, Zhao Chengyu finally just gave a low click of his tongue and stood up by pushing off his knees.

Walking two steps toward the formation, he turned back to add a sentence, his voice very soft—a sentiment only students of the same cohort could understand: "It's truly outrageous, being of the same cohort."

The instructor walked to the front of the square formation and blew the whistle sharply.

"Assemble!"

The formation quickly quieted down in an instant, all restlessness suppressed beneath the camouflage uniforms.

Roll call began.

"Zhao Chengyu."

"Here."

"Chen Qiming."

"Here."

"Jiang Lin."

"Here."

...

At the same time.

The traffic volume curve on the backend of the official website of the Mathematical Sciences Center, Tsinghua University, began an abnormally steep climb.

At eight-forty in the morning, the Mathematical Sciences Center published today's first academic update.

"Jiang Lin's Preprint on the Bridge between Finite Field Model PFR and Marton Entropy Forms Made Public"

The body text was entirely up to a very high-level academic announcement standard.

"The PFR / Marton v1.0 preprint submitted by Jiang Lin was made public early this morning. This manuscript had previously completed its main chain explanation in a closed-door technical report at the Mathematical Sciences Center. Having been independently verified by multiple scholars in related directions, within the scope of the Finite Field Model explicitly stated in the manuscript, the Polynomial Freiman-Ruzsa main proof chain holds; the Marton entropy form bridge-building part is logically self-consistent. The Mathematical Sciences Center will organize a series of thematic discussions in the near future for researchers in related directions to systematically digest the manuscript's structure."

Nine-thirty.

The homepage of Tsinghua University simultaneously published a news story.

"Jiang Lin Achieves Major Breakthrough in Finite Field Model PFR Direction"

The typesetting of the news was similarly rigorous.

The first paragraph objectively stated the research achievements.

The second paragraph listed the preprint publication status, preliminary feedback from top overseas scholars in related directions, and the systematic digestion seminars that the Mathematical Sciences Center would subsequently organize.

Then came the third paragraph.

"Jiang Lin is an undergraduate student of the Class of 2022 at Qiuzhen College, Tsinghua University. He once won the mathematics gold award at The 9th International Congress of Chinese Mathematicians and gained international attention through the construction of Jiangs Brick in the aperiodic tiling problem. Currently, the Shing-Tung Yau Mathematical Sciences Center, Tsinghua University, provides him with academic undertaking and research support."

Ten-twenty in the morning.

Inside the administrative building of Tsinghua University, an internal temporary coordination meeting was convened ahead of schedule.

The atmosphere in the meeting room was slightly solemn. Seated were several core leaders from the Mathematical Sciences Center, the main academic affairs teacher in charge of Qiuzhen College, and several administrative leaders at the university level.

The agenda of the meeting was not how to unify the external publicity talking points.

Nor was it whether or not to add any special arrangements for Jiang Lin.

This point had already been discussed and implemented as early as the admission stage, when Jiang Lin shocked the academic world with Jiangs Brick.

That spacious independent office on the second floor of the Mathematical Sciences Center, the singly allocated single apartment in Building 17 of Zijing Apartment, the twenty-four-hour unimpeded access control system, and the separate academic interfaces connecting directly to professors...

These were originally institutional buffers prepared for a non-standard, and one could even say extremely rare, genius student.

Yet now, this buffer was clearly no longer enough.

Everything that happened within these few hours after the PFR / Marton preprint was made public made everyone present realize that what Jiang Lin needed was far from being so-called special student treatment.

Instead, it was an institutional shell capable of undertaking an independent researcher who was mature and possessed immense influence.

A deputy director of the Mathematical Sciences Center pushed up his glasses and spoke very directly.

"The hardware of the office is not a problem."

"He already has one of the best offices in the entire center."

"The problem is that that office is currently just a quiet room. Sitting inside alone, he won't be able to cope with the upcoming situation."

"Therefore, what we need to consider is not adding another desk or a few high-configuration computers for him, but rather we must upgrade that room into a fully equipped research unit."

The meeting room fell quiet for a moment.

The academic affairs teacher's pen paused mid-air.

The deputy director spoke very specifically, and every single item hit the crucial point.

"Version management and subsequent revisions of the manuscript."

"Archiving and reply communication of massive international communications."

"Feedback organization and technical memos for the series of seminar classes to be conducted next."

"It might also involve the theorem formalization verification interface in cooperation with the Department of Computer Science."

"Reception of an endless stream of domestic and foreign visiting scholars."

"As well as the filtering of exponentially growing media, commercial, and administrative invitations every day."

"If the school hasn't established a dedicated support team for these matters, in the end, all these trivial, energy-consuming messes will fall back onto Jiang Lin himself. We cannot let someone capable of deriving PFR reply to those business emails."

The teacher from Qiuzhen College flipped through the thick student status notes in front of them and quietly reminded: "But from the perspective of rules and regulations, his student status is still in the college; he is still a freshman."

"His student status is of course in the college; that is an objective fact." The head of the Mathematical Sciences Center took over the conversation with a firm tone, "But within the scientific research system and administrative management, we can no longer simply register him merely as an undergraduate. Everyone knows it in their hearts: his current academic level is completely unsuited to be hung under the mentor name of any professor, nor could he possibly be a student member in any research group."

The head looked around the meeting room.

"He should have a separate file established."

"My suggestion is: with Jiang Lin as the individual core, establish an independent research unit, equipped with dedicated academic secretaries and administrative assistants."

As these words fell, several university-level leaders in the meeting room all raised their heads.

Research unit.

This was not a word that would appear in ordinary undergraduate training programs; it was closer to the support structure configured by the Mathematical Sciences Center for independent PIs.

This also meant that in terms of administrative establishment, Tsinghua University was no longer just providing a quiet environment for a genius student.

But rather acknowledging in black and white that this eighteen-year-old student himself already possessed the qualifications and equivalence to become the core of a cutting-edge research organization.

After a moment of silence, a person in charge from the Propaganda Department reminded: "If we make such an exception, what about the subsequent publicity talking points? The outside world might have over-interpretations."

"We are simply providing the academic undertaking environment we possess in accordance with the achievements."

The head of the Mathematical Sciences Center shook their head.

"This isn't making an exception; it should be called matching."